IJPAM: Volume 60, No. 3 (2010)

Abstract.Operators preserving the rank of
real matrices were studied in Basley [#!2!#] under assumption that the
operator is linear. In the present paper the linearity of the
operator is not assumed: we assume only that the operator is of
the form , where
are functions
for
. If the min{, then in the matrix space the operator preserving the rank of matrices must be
linear as in Basley [#!2!#]. If the min, then the operator may be
nonlinear. In both cases the forms of the operator are presented.